Distributed matrix multiplication for neural networks

ABSTRACT

In one embodiment, a matrix operation associated with a plurality of input matrices may be performed. The plurality of input matrices may be partitioned into a plurality of input partitions, wherein the plurality of input matrices is partitioned based on a number of available processing elements. The plurality of input partitions may be distributed among a plurality of processing elements, wherein each input partition is distributed to a particular processing element of the plurality of processing elements. A plurality of partial matrix operations may be performed using the plurality of processing elements, and partial matrix data may be transmitted between the plurality of processing elements while performing the plurality of partial matrix operations. A result of the matrix operation may be determined based on the plurality of partial matrix operations.

FIELD OF THE SPECIFICATION

This disclosure relates in general to the field of computer processing,and more particularly, though not exclusively, to performing matrixoperations using a plurality of processing resources.

BACKGROUND

Matrix operations, such as matrix multiplication and convolutions, canbe highly processor-intensive and memory-intensive operations, as theyoften involve complex operations on large, multi-dimensional matrixoperands. Accordingly, the performance of complex matrix operations canbe limited by the processing and/or memory latency. As matrix operationsare increasingly utilized in a variety of applications and withever-growing data sets (from graphics and image processing to machinelearning and artificial intelligence), the demand for high-performanceprocessing of matrix operations is increasing.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is best understood from the following detaileddescription when read with the accompanying figures. It is emphasizedthat, in accordance with the standard practice in the industry, variousfeatures are not necessarily drawn to scale, and are used forillustration purposes only. Where a scale is shown, explicitly orimplicitly, it provides only one illustrative example. In otherembodiments, the dimensions of the various features may be arbitrarilyincreased or reduced for clarity of discussion.

FIG. 1 illustrates a schematic diagram for an example computing systemaccording to certain embodiments.

FIGS. 2A-C illustrate block diagrams for an example embodiment of amatrix processing architecture.

FIGS. 3 and 4 illustrate block diagrams for example embodiments ofcomputer processors.

FIG. 5 illustrates an example of partitioning matrix operands.

FIGS. 6A-C illustrate an example weight update operation in a neuralnetwork.

FIGS. 7A-C illustrate an example forward propagation operation in aneural network.

FIGS. 8A-C illustrate an example backward propagation operation in aneural network.

FIG. 9 illustrates a flowchart for an example embodiment of distributedmatrix operations.

EMBODIMENTS OF THE DISCLOSURE

The following disclosure provides many different embodiments, orexamples, for implementing different features of the present disclosure.Specific examples of components and arrangements are described below tosimplify the present disclosure. These are, of course, merely examplesand are not intended to be limiting. Further, the present disclosure mayrepeat reference numerals and/or letters in the various examples. Thisrepetition is for the purpose of simplicity and clarity and does not initself dictate a relationship between the various embodiments and/orconfigurations discussed. Different embodiments may have differentadvantages, and no particular advantage is necessarily required of anyembodiment.

Matrix processing operations (e.g., linear algebra operations thatinvolve matrix and/or vector operands) have a wide range of applicationsin computing systems, from graphics processing to machine learning andartificial intelligence, among other examples. For example, complexmatrix operations may be used to implement artificial neural networksthat provide artificial intelligence and machine learning capabilities,including computer vision, autonomous navigation, speech and audiorecognition, and natural language processing, among other examples.These complex matrix operations (e.g., matrix multiplication andconvolutions) may be used to implement the fundamental operations ofneural networks, such as forward propagation, backward propagation, andweight updates. These matrix operations, however, can be highlyprocessor and memory intensive, as they often involve complex operationson large, multi-dimensional matrix operands. Accordingly, theperformance of these matrix operations can be limited by processingand/or memory latency. As matrix operations are increasingly utilized ina variety of applications with ever-growing data sets, such asartificial intelligence and machine learning, the demand forhigh-performance processing of matrix operations is increasing.

Existing matrix processing approaches suffer from variousinefficiencies, particularly when used to implement artificialintelligence and machine learning in artificial neural networks. Forexample, while central processing units (CPUs) could be used to performmatrix operations, many CPU architectures are designed for lowarithmetic intensity operations (i.e., a low ratio of arithmeticoperations relative to memory operations), and thus are not designed forefficient execution of matrix operations. Moreover, many CPUarchitectures utilize complex local or cache memory management routines,which may increase processing overhead and execution complexity foroperations involving large matrix operands. Graphics processing units(GPUs) could also be used to perform matrix operations. GPUs, however,are often designed for high precision computations and may provide alevel of precision that is unnecessary for certain matrix operations,thus reducing the volume of matrix operations that can be performed.Accordingly, existing matrix processing approaches are inefficient forcertain matrix operations, such as matrix multiplication or convolutionoperations involving large matrix operands and/or matrix operands withcertain dimensions, among other examples. The existing approaches areunable to perform these matrix operations with 100% processingefficiency using all available processing resources. Moreover, existingapproaches cannot be efficiently scaled to perform these matrixoperations across additional processing resources in parallel. As anexample, existing approaches are inefficient for matrix multiplication(e.g., general matrix multiplication or GEMM) on a large matrix operandwhich is neither square nor a single vector, such as a “thin” matrixwith a much larger height than width. Existing approaches require moretime to access and communicate the matrix operands than to perform theactual matrix computations, resulting in idle processing time whilematrix operands are being obtained from memory and/or communicated toprocessing resources. Similarly, existing approaches are inefficient forconvolution operations on large matrix operands, as they are unable toefficiently distribute or scale a convolution operation across avariable number of processing resources. Thus, existing approaches donot achieve 100% processing efficiency for these matrix operations.

The matrix processing functionality described throughout this disclosureperforms matrix operations using a distributed approach that achieves100% processing efficiency using the available processing resources. Forexample, this approach distributes matrix operations across multipleprocessing resources in a processing architecture that is optimized forperforming matrix operations, thus enabling full utilization of theprocessing resources throughout the duration of the matrix operations.For example, the processing architecture may include multiple processingresources that are designed and optimized for performing matrixoperations, and may support a higher volume of matrix operations thanother architectures (e.g., GPUs). In some embodiments, these processingresources may be configured in a cyclical arrangement, with eitherunidirectional communication interfaces between neighboring processingresources (a “single-cyclical” configuration) or bi-directionalcommunication interfaces between neighboring processing resources (a“dual-cyclical” configuration). In addition, the processing resourcesmay be arranged hierarchically with multiple levels of processingresources. For example, in some embodiments, the processing resourcesmay include multiple matrix processing chips, multiple high bandwidthmemory (HBM) modules and matrix processing clusters on each matrixprocessing chip, and/or multiple matrix processing units (MPUs) on eachmatrix processing cluster. This processing architecture enables matrixoperations to be distributed across multiple processing resources and/orprocessing hierarchies with 100% processing efficiency. In addition,this processing architecture enables matrix operations to be efficientlyscaled across a variable number of processing resources operating inparallel, while still achieving 100% processing efficiency.

As an example, in some embodiments, a matrix operation may bedistributed across multiple processing resources in a manner thatresults in the latency for communicating matrix operands being less thanthe matrix processing time, which allows the communication of matrixoperands to be completed while the matrix processing is being performed.For example, a dual-cyclical configuration of processing resourcesenables each processing resource to perform matrix computations whilesimultaneously obtaining matrix operands and data from both of itsneighboring processing resources, which significantly reduces thelatency for communicating matrix operands. The communication latency maybe reduced by half when using this dual-cyclical approach as opposed toa single-cyclical approach where each processing resource only obtainsmatrix operands and data from one neighboring processing resource at anygiven time. In this manner, the latency for communicating matrixoperands can be fully masked by the matrix processing time, thusavoiding any wasted or idle processing time and achieving 100%processing efficiency. Accordingly, matrix operations (e.g., matrixmultiplication or GEMM) can be performed efficiently even for largematrix operands and/or matrix operands with certain dimensions, such asa large matrix operand that is neither square nor a single vector (e.g.,a “thin” matrix with a much larger height than width).

The distributed matrix processing functionality described throughoutthis disclosure provides numerous technical advantages, includingalleviating the inefficiencies of existing approaches and enablingmatrix operations to be executed efficiently, achieving 100% processingefficiency using the available processing resources, and efficientlyscaling matrix operations across a variable number of processingresources operating in parallel. These advantages result in reducedprocessing time for matrix operations, which improves performance forapplications that involve complex matrix operations, such as artificialintelligence and machine learning functionality implemented usingartificial neural networks (e.g., convolutional neural networks,multilayer perceptrons (MLPs), restricted Boltzmann machines (RBM), anddeep belief networks (DBN), among other examples).

Example embodiments that may be used to implement the matrix processingfunctionality of this disclosure will now be described with moreparticular reference to the attached FIGURES.

FIG. 1 illustrates a schematic diagram for an example computing system100 according to certain embodiments.

In some embodiments, the matrix processing functionality describedthroughout this disclosure may be implemented in system 100. Matrixprocessing functionality may be used in system 100 for a wide range ofapplications and/or use cases involving matrix operations, from graphicsprocessing to machine learning and artificial intelligence, among otherexamples. For example, in some embodiments, matrix processingfunctionality may be used to implement artificial intelligence andmachine learning in artificial neural networks. Moreover, matrixprocessing functionality may be implemented by any component of system100. For example, in the illustrated embodiment, system 100 includesedge devices 110, cloud services 120, matrix processing nodes 130, andnetwork 150. Matrix processing nodes 130 may include any component ordevice with matrix processing functionality, including any component ofsystem 100. For example, matrix processing nodes 130 may include cloudservices 120 and/or servers implemented with matrix processingfunctionality (e.g., application servers in a datacenter), edge devices110 implemented with matrix processing functionality (e.g., end-userdevices 112, Internet-of-Things devices 114, gateways 116), and soforth. These various components of system 100 are discussed furtherbelow.

Edge devices 110 may include any equipment and/or devices deployed orconnected near the “edge” of a communication system 100. Edge devices110 may communicate with each other and/or with other remote networksand services (e.g., cloud services 120) through one or more networksand/or communication protocols, such as network 150. In someembodiments, certain edge devices 110 may include the matrix processingfunctionality described throughout this disclosure, and thus may be usedas matrix processing nodes 130. In the illustrated embodiment, edgedevices 110 include end-user devices 112 (e.g., desktops, laptops,mobile devices), Internet-of-Things (IoT) devices 114, and gatewaysand/or routers 116, among other examples.

End-user devices 112 may include any device that enables or facilitatesuser interaction with computing system 100, including, for example,desktop computers, laptops, tablets, mobile phones and other mobiledevices, and wearable devices (e.g., smart watches, smart glasses,headsets), among other examples.

IoT devices 114 may include any device capable of communicating and/orparticipating in an Internet-of-Things (IoT) system or network. IoTsystems may refer to new or improved ad-hoc systems and networkscomposed of multiple different devices (e.g., IoT devices 114)interoperating and synergizing for a particular application or use case.Such ad-hoc systems are emerging as more and more products and equipmentevolve to become “smart,” meaning they are controlled or monitored bycomputer processors and are capable of communicating with other devices.For example, an IoT device 114 may include a computer processor and/orcommunication interface to allow interoperation with other components ofsystem 100, such as with cloud services 120 and/or other edge devices110. IoT devices 114 may be “greenfield” devices that are developed withIoT capabilities from the ground-up, or “brownfield” devices that arecreated by integrating IoT capabilities into existing legacy devicesthat were initially developed without IoT capabilities. For example, insome cases, IoT devices 114 may be built from sensors and communicationmodules integrated in or attached to “things,” such as equipment, toys,tools, vehicles, living things (e.g., plants, animals, humans), and soforth. Alternatively, or additionally, certain IoT devices 114 may relyon intermediary components, such as edge gateways or routers 116, tocommunicate with the various components of system 100.

IoT devices 114 may include various types of sensors for monitoring,detecting, measuring, and generating sensor data and signals associatedwith characteristics of their environment. For instance, a given sensormay be configured to detect one or more respective characteristics, suchas movement, weight, physical contact, temperature, wind, noise, light,position, humidity, radiation, liquid, specific chemical compounds,battery life, wireless signals, computer communications, and bandwidth,among other examples. Sensors can include physical sensors (e.g.,physical monitoring components) and virtual sensors (e.g.,software-based monitoring components). IoT devices 114 may also includeactuators to perform various actions in their respective environments.For example, an actuator may be used to selectively activate certainfunctionality, such as toggling the power or operation of a securitysystem (e.g., alarm, camera, locks) or household appliance (e.g., audiosystem, lighting, HVAC appliances, garage doors), among other examples.

Indeed, this disclosure contemplates use of a potentially limitlessuniverse of IoT devices 114 and associated sensors/actuators. IoTdevices 114 may include, for example, any type of equipment and/ordevices associated with any type of system 100 and/or industry,including transportation (e.g., automobile, airlines), industrialmanufacturing, energy (e.g., power plants), telecommunications (e.g.,Internet, cellular, and television service providers), medical (e.g.,healthcare, pharmaceutical), food processing, and/or retail industries,among others. In the transportation industry, for example, IoT devices114 may include equipment and devices associated with aircrafts,automobiles, or vessels, such as navigation systems, autonomous flightor driving systems, traffic sensors and controllers, and/or any internalmechanical or electrical components that are monitored by sensors (e.g.,engines). IoT devices 114 may also include equipment, devices, and/orinfrastructure associated with industrial manufacturing and production,shipping (e.g., cargo tracking), communications networks (e.g.,gateways, routers, servers, cellular towers), server farms, electricalpower plants, wind farms, oil and gas pipelines, water treatment anddistribution, wastewater collection and treatment, and weathermonitoring (e.g., temperature, wind, and humidity sensors), among otherexamples. IoT devices 114 may also include, for example, any type of“smart” device or system, such as smart entertainment systems (e.g.,televisions, audio systems, videogame systems), smart household oroffice appliances (e.g., heat-ventilation-air-conditioning (HVAC)appliances, refrigerators, washers and dryers, coffee brewers), powercontrol systems (e.g., automatic electricity, light, and HVAC controls),security systems (e.g., alarms, locks, cameras, motion detectors,fingerprint scanners, facial recognition systems), and other homeautomation systems, among other examples. IoT devices 114 can bestatically located, such as mounted on a building, wall, floor, ground,lamppost, sign, water tower, or any other fixed or static structure. IoTdevices 114 can also be mobile, such as devices in vehicles oraircrafts, drones, packages (e.g., for tracking cargo), mobile devices,and wearable devices, among other examples. Moreover, an IoT device 114can also be any type of edge device 110, including end-user devices 112and edge gateways and routers 116.

Edge gateways and/or routers 116 may be used to facilitate communicationto and from edge devices 110. For example, gateways 116 may providecommunication capabilities to existing legacy devices that wereinitially developed without any such capabilities (e.g., “brownfield”IoT devices). Gateways 116 can also be utilized to extend thegeographical reach of edge devices 110 with short-range, proprietary, orotherwise limited communication capabilities, such as IoT devices 114with Bluetooth or ZigBee communication capabilities. For example,gateways 116 can serve as intermediaries between IoT devices 114 andremote networks or services, by providing a front-haul to the IoTdevices 114 using their native communication capabilities (e.g.,Bluetooth, ZigBee), and providing a back-haul to other networks 150and/or cloud services 120 using another wired or wireless communicationmedium (e.g., Ethernet, Wi-Fi, cellular). In some embodiments, a gateway116 may be implemented by a dedicated gateway device, or by a generalpurpose device, such as another IoT device 114, end-user device 112, orother type of edge device 110.

In some instances, gateways 116 may also implement certain networkmanagement and/or application functionality (e.g., IoT management and/orIoT application functionality for IoT devices 114), either separately orin conjunction with other components, such as cloud services 120 and/orother edge devices 110. For example, in some embodiments, configurationparameters and/or application logic may be pushed or pulled to or from agateway device 116, allowing IoT devices 114 (or other edge devices 110)within range or proximity of the gateway 116 to be configured for aparticular IoT application or use case.

Cloud services 120 may include services that are hosted remotely over anetwork 150, or in the “cloud.” In some embodiments, for example, cloudservices 120 may be remotely hosted on servers in datacenter (e.g.,application servers or database servers). Cloud services 120 may includeany services that can be utilized by or for edge devices 110, includingbut not limited to, data storage, computational services (e.g., dataanalytics, searching, diagnostics and fault management), securityservices (e.g., surveillance, alarms, user authentication), mapping andnavigation, geolocation services, network or infrastructure management,IoT application and management services, payment processing, audio andvideo streaming, messaging, social networking, news, and weather, amongother examples. In some embodiments, certain cloud services 120 mayinclude the matrix processing functionality described throughout thisdisclosure, and thus may be used as matrix processing nodes 130.

In general, edge devices 110 (and in particular IoT devices 114) maygenerate an extremely large volume and variety of data. IoT edge devices114 typically offload this data to the cloud for processing and/orstorage (e.g., by cloud services 120). Cloud services 120, however, maynot necessarily be suited to handle the rapidly growing volume, variety,and velocity of data generated by IoT devices 114 and other edge devices110. For example, cloud-based processing may not be ideal in certaincircumstances, such as processing time-sensitive or highly confidentialdata, or when faced with network bandwidth constraints, among otherexamples. In some embodiments, cloud services 120 may leverage “edge”based processing using edge devices 110 to improve the performance ofcloud services. Edge processing is an approach that involves processingcertain data at the network edge (e.g., using edge devices 110), nearwhere the data is generated, rather than simply funneling large volumesof data to the cloud for processing and storage. Certain data may stillbe sent to the cloud, as appropriate, such as for deeper analysis and/orlong-term storage. Edge processing may be used to complement theshortcomings of cloud-based processing (e.g., when cloud-basedprocessing is inefficient, ineffective, and/or unsecure), and thusimprove the handling of the growing volume, variety, and velocity ofdata generated by IoT devices 114 and/or other edge devices 110. Forexample, in some cases, processing data near its source (e.g., in thenetwork edge) rather than in the cloud may improve performance and/oravoid system failures or disasters. Edge processing may also conservenetwork bandwidth, which may be particularly beneficial when facingbandwidth constraints and/or limited network connectivity.

In some embodiments, edge devices 110 that provide edge-based processingfor cloud services 120 may be collectively referred to as the “fog,” asthey serve to extend the “cloud” to the edge of the network, thuscreating a “fog” over the network edge. In some embodiments, devices 110in the “fog” may connect and/or communicate with each other, forexample, using an interconnection standard or protocol. For example, insome embodiments, device interconnection may be implemented using theopen interconnect consortium (OIC) standard specification 1.0, releasedby the Open Connectivity Foundation™ (OCF) on Dec. 23, 2015, whichenables devices to discover and connect with each other. Anotherinterconnection protocol that may be used is Thread, a networkingprotocol for Internet-of-Things (IoT) devices used in “smart” homeautomation and similar deployments, which has been developed by analliance of organizations named the “Thread Group.” Otherinterconnection protocols may also be used, including, for example, theoptimized link state routing (OLSR) protocol, or the better approach tomobile ad-hoc networking (B.A.T.M.A.N.), among others.

Network 150 may be used to facilitate communication between thecomponents of computing system 100. For example, edge devices 110, suchas end-user devices 112 and IoT devices 114, may use network 150 tocommunicate with each other and/or access one or more remote cloudservices 120. Network 150 may include any number or type ofcommunication networks, including, for example, local area networks,wide area networks, public networks, the Internet, cellular networks,Wi-Fi networks, short-range networks (e.g., Bluetooth or ZigBee), and/orany other wired or wireless networks or communication mediums.

Any, all, or some of the computing devices of system 100 may be adaptedto execute any operating system, including Linux or other UNIX-basedoperating systems, Microsoft Windows, Windows Server, MacOS, Apple iOS,Google Android, or any customized and/or proprietary operating system,along with virtual machines adapted to virtualize execution of aparticular operating system.

While FIG. 1 is described as containing or being associated with aplurality of elements, not all elements illustrated within system 100 ofFIG. 1 may be utilized in each alternative implementation of the presentdisclosure. Additionally, one or more of the elements described inconnection with the examples of FIG. 1 may be located external to system100, while in other instances, certain elements may be included withinor as a portion of one or more of the other described elements, as wellas other elements not described in the illustrated implementation.Further, certain elements illustrated in FIG. 1 may be combined withother components, as well as used for alternative or additional purposesin addition to those purposes described herein.

Example Matrix Processing Architecture

FIGS. 2A-C illustrate block diagrams for an example embodiment of amatrix processing architecture.

In some embodiments, the matrix processing functionality describedthroughout this disclosure may be implemented using a matrix processingarchitecture, such as the matrix processing architecture of FIGS. 2A-2C.Matrix processing architectures, such as the matrix processingarchitecture of FIGS. 2A-2C, may be implemented or used in a variety ofsystems, devices, and/or components, such as those described throughoutthis disclosure, including system 100 of FIG. 1 and/or any of itsassociated components (e.g., cloud services 120/datacenter servers, edgedevices 110, matrix processing nodes 130). In some embodiments, thematrix processing architecture of FIGS. 2A-2C may be used to implementartificial intelligence and machine learning in neural networks. Thematrix processing architecture illustrated in FIGS. 2A-2C is merely oneexample embodiment for performing the matrix processing functionalitydescribed throughout this disclosure. Other embodiments may usedifferent types, arrangements, and/or numbers of components. Forexample, other embodiments may include any number of matrix processingchips 220, matrix processing clusters 230, matrix processing units(MPUs) 234, high bandwidth memory (HBM) modules 240, and/or memoryresource blocks (MRBs) 238. Moreover, all or part of any component ofthe matrix processing architecture of FIGS. 2A-2C (e.g., any componentof matrix processing system 200, matrix processing chips 220, and/ormatrix processing clusters 230) may be implemented as a separate orstand-alone component or chip, or may be integrated with othercomponents or chips, such as a system-on-a-chip (SoC) that integratesvarious computer components into a single chip.

FIG. 2A illustrates a block diagram for an example embodiment of amatrix processing system 200. In the illustrated embodiment, matrixprocessing system 200 includes host processor 260, host memory 270,matrix processing resources 210, and interconnect bus 280.

Host processor 260 may be configured to control and/or manage matrixprocessing system 200. For example, in some embodiments, host processor260 may use matrix processing resources 210 to perform complex matrixoperations. Host processor 260 may be any processing resource capable ofcontrolling and/or managing matrix processing functionality of matrixprocessing system 200. For example, in some embodiments, host processor260 may be implemented using computer processors 300 or 400 of FIGS. 3and 4, respectively. In some embodiments, host processor 260 may be aseparate or stand-alone component that is communicatively coupled tomatrix processing resources 210. Alternatively, in other embodiments,host processor 260 and matrix processing resources 210 may be integratedinto the same component or chip. For example, in some embodiments, thecomponents of matrix processing system 200, including host processor 260and matrix processing resources 210, may be implemented as asystem-on-a-chip (SoC).

Host memory 270 may include any type or combination of volatile and/ornon-volatile memory. Examples of volatile memory include various typesof random access memory (RAM), such as dynamic random access memory(DRAM), synchronous dynamic random access memory (SDRAM), and staticrandom access memory (SRAM), among other examples. Examples ofnon-volatile memory include disk-based storage mediums (e.g., magneticand/or optical storage mediums), solid-state storage (e.g., any form ofpersistent flash memory, including planar or three dimensional (3D) NANDflash memory or NOR flash memory), 3D crosspoint memory, electricallyerasable programmable read-only memory (EEPROM), and/or other types ofnon-volatile random access memories (RAM), among other examples. Hostmemory 270 may be used, for example, to store information for hostprocessor 260 during execution, such as code and/or data.

Interconnect bus 280 may be used, in some embodiments, tocommunicatively couple host processor 260 and host memory 270 to matrixprocessing resources 210. Interconnect bus 280 may use anyinterconnection protocol, such as Peripheral Component Interconnectexpress (PCIe), Universal Serial Bus (USB), or Small Computer SystemsInterface (SCSI), among other examples.

Matrix processing resources 210 may include any processing resourcesconfigured to perform matrix operations. For example, matrix processingresources 210 may be configured to perform matrix multiplicationoperations, convolution operations, element-wise matrix operations(e.g., +, *, /<, >, ==), dimension shuffle operations, and/or anycombination thereof. In some embodiments, matrix processing resources210 may include processing resources that are designed and optimized forperforming matrix operations. In some embodiments, matrix processingresources 210 may also be arranged hierarchically with multiple levelsof processing resources. For example, in the illustrated embodiment,matrix processing resources 210 include a plurality of matrix processingchips 220, and may also include any processing resources within eachmatrix processing chip 220. For example, as discussed below inconnection with FIGS. 2B and 2C, each matrix processing chip 220 mayinclude a plurality of high bandwidth memory (HBM) modules 240 and aplurality of matrix processing clusters 230, and each matrix processingcluster 230 may include multiple matrix processing units 234. Thus, insome embodiments, matrix processing resources 210 may include multiplematrix processing chips 220, multiple high bandwidth memory (HBM)modules 240 and multiple matrix processing clusters 230 on each matrixprocessing chip 220, and/or multiple matrix processing units 234 on eachmatrix processing cluster 230.

Matrix processing chips 220 may be, for example, any chips or othercomponents configured to perform matrix operations. For example, in someembodiments, a matrix processing chip 220 may be a peripheral card orchip connected to host processor 260 using any type of interconnectinterface, such as a PCIe interface. In some embodiments, a matrixprocessing chip 220 may be implemented using an integrated circuit, suchas an application specific integrated circuit (ASIC), a fieldprogrammable gate array (FPGA), and/or any other type of circuitry. Inthe illustrated embodiment, matrix processing chips 220 are configuredin a cyclical arrangement, with communication channels 215 betweenneighboring matrix processing chips 220. In some embodiments,communication channels 215 may provide one-way communication betweenneighboring matrix processing chips 220. In other embodiments, however,communication channels 215 may provide bi-directional communicationbetween neighboring matrix processing chips 220. A cyclical arrangementwith unidirectional communication between neighboring processingresources may be referred to as a “single-cyclical” configuration, whilea cyclical arrangement with bi-directional communication betweenneighboring processing resources may be referred to as a “dual-cyclical”configuration.

FIG. 2B illustrates a block diagram for an example embodiment of amatrix processing chip 220. In the illustrated embodiment, matrixprocessing chip 220 includes controller 222, host interface 224,inter-chip links 225, high bandwidth memory (HBM) modules 240, andmatrix processing clusters 230.

Controller 222 may be configured to control and/or manage matrixoperations performed by matrix processing chip 220. In some embodiments,controller 222 may control and/or manage matrix operations inconjunction with host processor 260 of FIG. 2A and/or master controlCPUs (MCCs) 232 of matrix processing clusters 230 of FIG. 2C. Forexample, in some embodiments, host processor 260, controller 222, and/ormaster control CPUs (MCCs) 232 may be configured to receive a matrixoperation or command, and distribute the matrix operation and matrixoperands across matrix processing clusters 230 and high bandwidth memory(HBM) modules 240. In some embodiments, controller 222 may be amicroprocessor, an integrated circuit, and/or any other type ofcircuitry and/or processing logic.

Host interface 224 may be a communication interface that enables amatrix processing chip 220 to communicate with host processor 260 ofFIG. 2A. In some embodiments, for example, controller 222 may use hostinterface 224 to communicate with host processor 260 of FIG. 2A. Hostinterface 224 may use any type of interconnect protocol or interface,including Peripheral Component Interconnect express (PCIe), UniversalSerial Bus (USB), or Small Computer Systems Interface (SCSI), amongother examples.

Inter-chip links (ICLs) 225 may enable a matrix processing chip 220 tocommunicate with other matrix processing chips. For example, inter-chiplinks 225 may be used to implement the communication channels 215between matrix processing chips 220 in FIG. 2A. An inter-chip link 225may be, for example, any communication interface that enables a matrixprocessing chip 220 to communicate with another matrix processing chip.In some embodiments, a matrix processing chip 220 may include multipleinter-chip links 225 (e.g., twelve inter-chip links). In someembodiments, an inter-chip link 225 may be implemented using one or moreserializer/de-serializer (SerDes) interfaces. A SerDes interface may bea communication interface that converts data from serial to parallel,and vice-versa. For example, the transmitter of a SerDes interface mayinclude a serial-to-parallel converter, and the receiver of a SerDesinterface may include a parallel-to-serial converter. In someembodiments, a matrix processing chip 220 may use multiple SerDesinterfaces for each connection to another matrix processing chip (e.g.,four SerDes interfaces between each pair of connected matrix processingchips).

High bandwidth memory (HBM) modules 240 may be memory componentsassociated with matrix processing chip 220 that are used to store matrixoperands and other matrix data. In some embodiments, high bandwidthmemory (HBM) modules 240 may be designed to efficiently store andretrieve matrix data. In some embodiments, high bandwidth memory (HBM)modules 240 may be multi-dimensional memory components configured tostore and retrieve data in multiple dimensions. For example, in someembodiments, high bandwidth memory (HBM) modules 240 may be memorycomponents configured to store and retrieve data in two dimensions, suchas rows and columns. Other embodiments, however, may use memorycomponents configured to store and retrieve data using any other numberof dimensions (e.g., one dimension, three dimensions, four dimensions,and so forth). In the illustrated embodiment, matrix processing chip 220includes four high bandwidth memory (HBM) modules 240 a-d. In someembodiments, high bandwidth memory (HBM) modules 240 may be shared bythe matrix processing clusters 230 of a matrix processing chip 220.

Matrix processing clusters 230 may include processing resourcesconfigured to perform matrix operations, such as matrix multiplication,convolutions, and/or dimension shuffling, among other examples. In someembodiments, matrix processing clusters 230 may be collectively used toexecute a particular matrix operation by performing matrix processing inparallel. In the illustrated embodiment, matrix processing chip 220includes twelve matrix processing clusters 230 a-I. Moreover, in theillustrated embodiment, matrix processing clusters 230 are configured orarranged using a two-dimensional mesh interconnection topology. Theinterconnection topology of matrix processing clusters 230 mayfacilitate cyclical communication among the matrix processing clusters230. Moreover, other embodiments may include any number and/orarrangement of matrix processing clusters 230.

FIG. 2C illustrates a block diagram for an example embodiment of amatrix processing cluster 230. In the illustrated embodiment, matrixprocessing cluster 230 includes master control CPU (MCC) 232, matrixprocessing units (MPUs) 234, slicing engine 236, and memory resourceblocks (MRBs) 238.

Master control CPU (MCC) 232 may be configured to control and/or managematrix operations performed by a matrix processing cluster 230. In someembodiments, master control CPU 232 may be a microprocessor, anintegrated circuit, and/or any other type of circuitry and/or processinglogic. In some embodiments, master control CPU 232 may receiveinstructions from another component, such as host processor 260 of FIG.2A and/or controller 222 of FIG. 2B. Based on the instructions, mastercontrol CPU 232 may then use matrix processing units 234 to performmatrix operations, such as matrix multiplication, convolutions, and/ordimension shuffling, among other examples. For example, master controlCPU 232 may receive an instruction to perform a matrix multiplicationoperation, such as C=A*B. The instruction may include the handles oridentifiers for each matrix, and may also indicate how the matricesshould be stored in memory resource blocks (MRBs) 238. Matrices A and Bmay then be broken down into a series of smaller matrices (e.g., 32×32matrices). Matrix operations may then be performed on the smallermatrices, and the partial results may be stored in memory resourceblocks (MRBs) 238, until the output matrix C has been fully computed.

Matrix processing units (MPUs) 234 may be configured to perform matrixoperations, such as matrix multiplication, convolutions, and/ordimension shuffling. In some embodiments, matrix processing units (MPUs)234 perform matrix operations based on commands received from mastercontrol CPU (MCC) 232. Moreover, in some embodiments, each matrixprocessing cluster 230 may include multiple matrix processing units(MPUs) 234. For example, in the illustrated embodiment, matrixprocessing cluster 230 includes two matrix processing units (MPUs) 234.A matrix processing unit (MPU) 234 may be capable of performing matrixoperations, such as matrix multiplication, on small matrices (e.g.,32×32 matrices). In some cases, a matrix processing unit (MPU) 234 maybe designed and/or optimized to perform matrix multiplicationoperations. A matrix processing unit (MPU) 234 may load matrix operandsfrom memory resource blocks (MRBs) 238. In some embodiments, a matrixprocessing unit (MPU) 234 may support the following arithmeticoperations: matrix multiplication; unary matrix operations; binarymatrix operations, such as addition (+), subtraction (−), multiplication(*), division (/), bitwise XOR, AND, OR, logical and arithmetic left andright shift, comparison (>, <, >=, <=, ==, !=); and column-wise,row-wise, and matrix-wide operations, such as sum, max value, and minvalue.

Slicing engine 236 may be configured to slice the matrix operands of aparticular matrix operation into smaller partial matrices. For example,in some embodiments, master control CPU (MCC) 232 may use slicing engine236 to break up matrix operands into smaller partial matrices for matrixprocessing units (MPUs) 234. In some embodiments, slicing engine 236 mayinclude a convolution slicing engine (CSE) to perform matrix slicing forconvolution operations. For example, in some embodiments, a convolutionslicing engine (CSE) may slice matrix operands in a manner that enablesa convolution operation to be cast as a matrix multiplication operation,thus enabling the same processing logic to perform both matrixmultiplication and convolution operations. Moreover, in someembodiments, slicing engine 236 and/or the associated convolutionslicing engine (CSE) may be used to perform the dimension shuffleoperations to reorder the dimensions of a matrix.

Memory resource blocks (MRBs) 238 may be memory components on matrixprocessing cluster 230 used to store matrix operands and other matrixdata. In some embodiments, memory resource blocks (MRBs) 238 may bedesigned to store and retrieve matrix data efficiently. In someembodiments, memory resource blocks (MRBs) 238 may be multi-dimensionalmemory components configured to store and retrieve data in multipledimensions. For example, in some embodiments, memory resource blocks(MRBs) 238 may be memory components configured to store and retrievedata in two dimensions, such as rows and columns. In the illustratedembodiment, matrix processing cluster 230 includes ten memory resourceblocks (MRBs) 238. Other embodiments, however, may include a differentnumber of memory resource blocks (MRBs) 238 on a matrix processingcluster 230. In some embodiments, each memory resource block (MRB) 238may be capable of storing a matrix of a certain size (e.g., a 256×512matrix). In some embodiments, memory resource blocks (MRBs) 238 may beshared by the matrix processing units (MPUs) 234 of a particular matrixprocessing cluster 230.

In some embodiments, the matrix processing architecture of FIGS. 2A-2Cmay be used to implement the matrix processing functionality describedthroughout this disclosure. For example, matrix processing system 200may be used to perform matrix operations using a distributed approachthat achieves 100% processing efficiency using the available processingresources. For example, in some embodiments, a matrix operation may bedistributed across multiple processing resources 210 that are optimizedfor matrix processing, thus enabling full utilization of the processingresources 210 throughout the duration of the matrix operation. Forexample, matrix processing system 200 may include multiple processingresources 210 that are designed and optimized for performing matrixoperations. In some embodiments, these processing resources 210 may beconfigured in a single-cyclical or dual-cyclical arrangement. Inaddition, the processing resources 210 may be arranged hierarchicallywith multiple levels of processing resources. For example, in someembodiments, the processing resources 210 may include multiple matrixprocessing chips 220, multiple high bandwidth memory (BHM) modules 240and multiple matrix processing clusters 230 on each matrix processingchip 220, and/or multiple matrix processing units (MPUs) 234 on eachmatrix processing cluster 230. This processing architecture enablesmatrix operations to be distributed across multiple processing resources210 and/or processing hierarchies with 100% processing efficiency. Inaddition, this processing architecture enables matrix operations to beefficiently scaled across a variable number of processing resources 210operating in parallel, while still achieving 100% processing efficiency.For example, scaling may be achieved by adjusting the number ofprocessing resources 210 used to perform a particular matrix operation,such as the number of matrix processing systems 200 or servers, thenumber of matrix processing chips 220 in each matrix processing system200 or server, and so forth.

As an example, the matrix processing architecture of FIGS. 2A-2C may beused to implement matrix multiplication and/or convolution operations.For example, in some embodiments, a matrix multiplication operation maybe distributed across multiple processing resources 210 in a manner thatresults in the latency for communicating matrix operands being less thanthe matrix processing time, which allows the communication of matrixoperands to be completed while the matrix processing is being performed.For example, for certain matrix operations involving matrix operandswith certain dimensions (e.g., matrix multiplication with a “thin”matrix operand), the time required to access and communicate matrixoperands may exceed the time required to perform the actual matrixcomputations, resulting in idle processing time while the matrixoperands are being obtained from memory and/or communicated toprocessing resources 210. For example, a single-cyclical configuration(e.g., where each processing resource 210 only obtains matrix operandsand data from one neighboring processing resource 210 at any given time)may be unable to achieve 100% processing efficiency for these particulartypes of matrix operations and matrix operands. However, a dual-cyclicalconfiguration of processing resources 210 enables each processingresource to perform matrix computations while simultaneously obtainingmatrix operands and data from both of its neighboring processingresources 210, which significantly reduces the latency for communicatingmatrix operands, and thus avoids any idle processing time. For example,the communication latency for certain operations may be reduced by halfwhen using a dual-cyclical approach as opposed to a single-cyclicalapproach. In this manner, the latency for communicating matrix operandsand matrix data can be fully masked by the matrix processing time, thusavoiding any wasted or idle processing time and achieving 100%processing efficiency. Accordingly, matrix operations (e.g., matrixmultiplication or GEMM) can be performed efficiently even for largematrix operands and/or matrix operands with certain dimensions, such asa large matrix operand that is neither square nor a single vector (e.g.,a “thin” matrix with a much larger height than width). For example,matrix multiplication can be performed efficiently even when multiplyingtwo thin matrices, a thin matrix and a square matrix, and so forth.Similarly, convolution operations may be distributed across multipleprocessing resources 210 in a manner that results in 100% processingefficiency using the available processing resources.

As an example, when a matrix operation or command is received, thematrix operation may be distributed across the processing resources 210of matrix processing system 200. For example, the matrix operands (orinput matrices) may be partitioned based on the number of availableprocessing resources 210. Moreover, in some embodiments, the partitionsmay be across the rows of the matrix operands, and/or across any otherdimension of the matrix operands. Each partition may then be distributedto a particular processing resource 210. Each processing resource 210may then perform a plurality of partial matrix operations. In someembodiments, the plurality of partial matrix operations is performed ina plurality of stages. For example, each processing resource 210 mayperform a particular stage of partial matrix operations whilesimultaneously sending and receiving partial matrix data to and from itsneighboring processing resources 210. For example, in a single-cyclicalconfiguration of processing resources 210, each processing resource 210either sends or receives partial matrix data to or from each neighboringprocessing resource 210. Similarly, in a dual-cyclical configuration ofprocessing resources 210, each processing resource 210 may send andreceive partial matrix data to and from each neighboring processingresource 210. Each processing resource 210 may then use the partialmatrix data for subsequent partial matrix operations. The result of thematrix operation may then be determined based on the partial matrixoperations collectively performed by the processing resources 210.

Moreover, if the processing resources 210 are arranged hierarchically,the matrix operation may be distributed in a hierarchical manner. Forexample, the matrix operands (or input matrices) may initially bepartitioned based on the number of available matrix processing chips220. Each partition, and the associated partial matrix operations, maythen be distributed to a particular matrix processing chip 220. Thepartition and partial matrix operations distributed to a particularmatrix processing chip 220 may then be similarly partitioned anddistributed across the matrix processing clusters 230 and/or highbandwidth memory (HBM) modules 240 of the particular matrix processingchip 220. For example, for certain matrix operations, partial matrixoperations may be distributed to each matrix processing cluster 230.Alternatively, for certain matrix operations, partial matrix operationsmay be distributed across various “logical processing nodes” (e.g.,groups of matrix processing clusters 230 associated with ahigh-bandwidth memory (HBM) module 240), and may then be distributed toeach matrix processing cluster 230 of a particular logical processingnode. In some embodiments, the matrix processing clusters 230 (and/orthe logical processing nodes) may be cyclically configured similar tothe matrix processing chips 220. The partition and partial matrixoperations distributed to a particular matrix processing cluster 230 maythen be similarly partitioned and distributed across the matrixprocessing units (MPUs) 234 of the particular matrix processing cluster230.

Example Computer Processor Architectures

FIGS. 3 and 4 illustrate block diagrams for example embodiments ofcomputer processors that may be used in accordance with embodimentsdisclosed herein. For example, the computer processors illustrated inFIGS. 3 and 4 may be used as host processors associated with matrixprocessing systems (e.g., host processor 260 in matrix processing system200 of FIG. 2A), or as processors associated with other componentsand/or devices discussed throughout this disclosure (e.g., processorsassociated with components in system 100 of FIG. 1). Other processor andsystem designs and configurations known in the art for laptops,desktops, handheld PCs, personal digital assistants, engineeringworkstations, servers, network devices, network hubs, switches, embeddedprocessors, digital signal processors (DSPs), graphics devices, videogame devices, set-top boxes, micro controllers, cell phones, portablemedia players, hand held devices, and various other electronic devices,are also suitable. In general, a huge variety of systems or electronicdevices capable of incorporating a processor and/or other executionlogic as disclosed herein are generally suitable.

FIG. 3 illustrates a block diagram for an example embodiment of aprocessor 300. Processor 300 is an example of a type of hardware devicethat can be used in connection with the embodiments described throughoutthis disclosure. Processor 300 may be any type of processor, such as amicroprocessor, an embedded processor, a digital signal processor (DSP),a network processor, a multi-core processor, a single core processor, orother device to execute code. Although only one processor 300 isillustrated in FIG. 3, a processing element may alternatively includemore than one of processor 300 illustrated in FIG. 3. Processor 300 maybe a single-threaded core or, for at least one embodiment, the processor300 may be multi-threaded in that it may include more than one hardwarethread context (or “logical processor”) per core.

FIG. 3 also illustrates a memory 302 coupled to processor 300 inaccordance with an embodiment. Memory 302 may be any of a wide varietyof memories (including various layers of memory hierarchy) as are knownor otherwise available to those of skill in the art. Such memoryelements can include, but are not limited to, random access memory(RAM), read only memory (ROM), logic blocks of a field programmable gatearray (FPGA), erasable programmable read only memory (EPROM), andelectrically erasable programmable ROM (EEPROM).

Processor 300 can execute any type of instructions associated withalgorithms, processes, or operations detailed herein. Generally,processor 300 can transform an element or an article (e.g., data) fromone state or thing to another state or thing.

Code 304, which may be one or more instructions to be executed byprocessor 300, may be stored in memory 302, or may be stored insoftware, hardware, firmware, or any suitable combination thereof, or inany other internal or external component, device, element, or objectwhere appropriate and based on particular needs. In one example,processor 300 can follow a program sequence of instructions indicated bycode 304. Each instruction enters a front-end logic 306 and is processedby one or more decoders 308. The decoder may generate, as its output, amicro operation such as a fixed width micro operation in a predefinedformat, or may generate other instructions, microinstructions, orcontrol signals that reflect the original code instruction. Front-endlogic 306 may also include register renaming logic and scheduling logic,which generally allocate resources and queue the operation correspondingto the instruction for execution.

Processor 300 can also include execution logic 314 having a set ofexecution units 316 a, 316 b, 316 n, etc. Some embodiments may include anumber of execution units dedicated to specific functions or sets offunctions. Other embodiments may include only one execution unit or oneexecution unit that can perform a particular function. Execution logic314 performs the operations specified by code instructions.

After completion of execution of the operations specified by the codeinstructions, back-end logic 318 can retire the instructions of code304. In one embodiment, processor 300 allows out of order execution butrequires in order retirement of instructions. Retirement logic 320 maytake a variety of known forms (e.g., re-order buffers or the like). Inthis manner, processor 300 is transformed during execution of code 304,at least in terms of the output generated by the decoder, hardwareregisters and tables utilized by register renaming logic 310, and anyregisters (not shown) modified by execution logic 314.

Although not shown in FIG. 3, a processing element may include otherelements on a chip with processor 300. For example, a processing elementmay include memory control logic along with processor 300. Theprocessing element may include I/O control logic and/or may include I/Ocontrol logic integrated with memory control logic. The processingelement may also include one or more caches. In some embodiments,non-volatile memory (such as flash memory or fuses) may also be includedon the chip with processor 300.

FIG. 4 illustrates a block diagram for an example embodiment of amultiprocessor 400. As shown in FIG. 4, multiprocessor system 400 is apoint-to-point interconnect system, and includes a first processor 470and a second processor 480 coupled via a point-to-point interconnect450. In some embodiments, each of processors 470 and 480 may be someversion of processor 300 of FIG. 3.

Processors 470 and 480 are shown including integrated memory controller(IMC) units 472 and 482, respectively. Processor 470 also includes aspart of its bus controller units point-to-point (P-P) interfaces 476 and478; similarly, second processor 480 includes P-P interfaces 486 and488. Processors 470, 480 may exchange information via a point-to-point(P-P) interface 450 using P-P interface circuits 478, 488. As shown inFIG. 4, IMCs 472 and 482 couple the processors to respective memories,namely a memory 432 and a memory 434, which may be portions of mainmemory locally attached to the respective processors.

Processors 470, 480 may each exchange information with a chipset 490 viaindividual P-P interfaces 452, 454 using point to point interfacecircuits 476, 494, 486, 498. Chipset 490 may optionally exchangeinformation with the coprocessor 438 via a high-performance interface439. In one embodiment, the coprocessor 438 is a special-purposeprocessor, such as, for example, a high-throughput MIC processor, anetwork or communication processor, compression engine, graphicsprocessor, GPGPU, embedded processor, matrix processor, or the like.

A shared cache (not shown) may be included in either processor oroutside of both processors, yet connected with the processors via P-Pinterconnect, such that either or both processors' local cacheinformation may be stored in the shared cache if a processor is placedinto a low power mode.

Chipset 490 may be coupled to a first bus 416 via an interface 496. Inone embodiment, first bus 416 may be a Peripheral Component Interconnect(PCI) bus, or a bus such as a PCI Express bus or another thirdgeneration I/O interconnect bus, although the scope of this disclosureis not so limited.

As shown in FIG. 4, various I/O devices 414 may be coupled to first bus416, along with a bus bridge 418 which couples first bus 416 to a secondbus 420. In one embodiment, one or more additional processor(s) 415,such as coprocessors, high-throughput MIC processors, GPGPU's,accelerators (such as, e.g., graphics accelerators or digital signalprocessing (DSP) units), matrix processors, field programmable gatearrays, or any other processor, are coupled to first bus 416. In oneembodiment, second bus 420 may be a low pin count (LPC) bus. Variousdevices may be coupled to a second bus 420 including, for example, akeyboard and/or mouse 422, communication devices 427 and a storage unit428 such as a disk drive or other mass storage device which may includeinstructions/code and data 430, in one embodiment. Further, an audio I/O424 may be coupled to the second bus 420. Note that other architecturesare possible. For example, instead of the point-to-point architecture ofFIG. 4, a system may implement a multi-drop bus or other sucharchitecture.

All or part of any component of FIG. 4 may be implemented as a separateor stand-alone component or chip, or may be integrated with othercomponents or chips, such as a system-on-a-chip (SoC) that integratesvarious computer components into a single chip.

Embodiments of the mechanisms disclosed herein may be implemented inhardware, software, firmware, or a combination of such implementationapproaches. Certain embodiments may be implemented as computer programsor program code executing on programmable systems comprising at leastone processor, a storage system (including volatile and non-volatilememory and/or storage elements), at least one input device, and at leastone output device.

Program code, such as code 430 illustrated in FIG. 4, may be applied toinput instructions to perform the functions described herein andgenerate output information. The output information may be applied toone or more output devices, in known fashion. For purposes of thisapplication, a processing system includes any system that has aprocessor, such as, for example; a digital signal processor (DSP), amicrocontroller, an application specific integrated circuit (ASIC), or amicroprocessor.

The program code may be implemented in a high level procedural or objectoriented programming language to communicate with a processing system.The program code may also be implemented in assembly or machinelanguage, if desired. In fact, the mechanisms described herein are notlimited in scope to any particular programming language. In any case,the language may be a compiled or interpreted language.

One or more aspects of at least one embodiment may be implemented byrepresentative instructions stored on a machine-readable medium whichrepresents various logic within the processor, which when read by amachine causes the machine to fabricate logic to perform the techniquesdescribed herein. Such representations, known as “IP cores” may bestored on a tangible, machine readable medium and supplied to variouscustomers or manufacturing facilities to load into the fabricationmachines that actually make the logic or processor.

Such machine-readable storage media may include, without limitation,non-transitory, tangible arrangements of articles manufactured or formedby a machine or device, including storage media such as hard disks, anyother type of disk including floppy disks, optical disks, compact diskread-only memories (CD-ROMs), compact disk rewritable's (CD-RWs), andmagneto-optical disks, semiconductor devices such as read-only memories(ROMs), random access memories (RAMs) such as dynamic random accessmemories (DRAMs), static random access memories (SRAMs), erasableprogrammable read-only memories (EPROMs), flash memories, electricallyerasable programmable read-only memories (EEPROMs), phase change memory(PCM), magnetic or optical cards, or any other type of media suitablefor storing electronic instructions.

Accordingly, embodiments of this disclosure also include non-transitory,tangible machine-readable media containing instructions or containingdesign data, such as Hardware Description Language (HDL), which definesstructures, circuits, apparatuses, processors and/or system featuresdescribed herein. Such embodiments may also be referred to as programproducts.

Distributed Matrix Operations

FIGS. 5, 6A-C, 7A-C, and 8A-C illustrate example operations in a neuralnetwork. In some embodiments, these example operations may be performedusing a matrix processing architecture, such as the matrix processingarchitecture of FIGS. 2A-2C. The fundamental operations of a neuralnetwork may include forward propagation, backward propagation, andweight updates. These operations may be used, in some embodiments, totrain a neural network in order to provide machine learningfunctionality. For example, a forward propagation operation may includepropagating a particular input through a neural network in order togenerate a corresponding output. The input to the forward propagationoperation may be a training pattern with a known or expected output. Abackward propagation operation may then be used to determine the errorassociated with the forward propagation operation based on thedifference or delta between the calculated output and the expectedoutput of the forward propagation operation. A weight update operationmay then be used to determine updated weight values in order to minimizethe associated error. In some embodiments, these neural networkoperations may be performed using matrix operations. For example, theinput values, weights, and output values may be represented usingmatrices. In some embodiments, these neural network operations may beimplemented using the following formulas:forward propagation: A ₂ =w*A ₁backward propagation: A ₁ =w ^(T) *A ₂weight update: Δw=A ₁ ^(T) *A ₂

FIG. 5 illustrates an example of partitioning matrix operands. Matrixoperands may be partitioned, for example, to perform matrix operationsusing the distributed matrix processing functionality describedthroughout this disclosure. In particular, matrix partitioning may beperformed for neural network operations, such as those illustrated inFIGS. 6, 7, and 8.

The illustrated embodiment demonstrates matrix partitioning for a weightmatrix (W) and an activation matrix (A). In the illustrated embodiment,weight matrix (W) and activation matrix (A) are partitioned into Ppartitions. In some embodiments, matrix operands may be partitioned intoa number of partitions corresponding to the number of availableprocessing resources. For example, weight matrix (W) and activationmatrix (A) may be partitioned into P partitions corresponding to Pprocessing resources. Moreover, in some embodiments, the matrix operandsmay be partitioned across their rows. Each partition may then bedistributed to a particular processing resource, as described throughoutthis disclosure.

In some embodiments, matrix operands may be partitioned hierarchicallybased on the hierarchical arrangement of processing resources. Forexample, the matrix operands may initially be partitioned based on thenumber of available matrix processing chips (e.g., matrix processingchips 220 of FIG. 2A). Each partition, and the associated partial matrixoperations, may then be distributed to a particular matrix processingchip. The partition and partial matrix operations distributed to aparticular matrix processing chip may then be similarly partitioned anddistributed across the matrix processing clusters of that matrixprocessing chip (e.g., matrix processing clusters 230 of FIG. 2B). Thepartition and partial matrix operations distributed to a particularmatrix processing cluster may then be similarly partitioned anddistributed across the matrix processing units (MPUs) of that matrixprocessing cluster (e.g., matrix processing units (MPUs) 234 of FIG.2C).

FIGS. 6A-C illustrate an example weight update operation in a neuralnetwork. FIG. 6A illustrates the weight update operation that is to beperformed, and FIGS. 6B and 6C illustrate how the weight updateoperation is performed.

FIG. 6A illustrates the following operation: A*B=C. A weight updateoperation may be implemented using the formula Δw=A₁ ^(T)*A₂, which maytranslate as follows in FIG. 6A: matrix A corresponds to A₁ ^(T) (e.g.,the transpose of the first activation matrix); matrix B corresponds toA₂ (e.g., the second activation matrix); and matrix C corresponds to Δw(e.g., the updated weight matrix).

Matrices A and B may first be partitioned based on the number ofavailable processing resources, as described in connection with FIG. 5.For example, in some embodiments, matrices A and B may be partitionedinto P partitions corresponding to the number of available matrixprocessing chips (e.g., matrix processing chips 220 of FIG. 2A). Forexample, if there are P matrix processing chips, the rows of matrix Amay be partitioned into partitions a₁-a_(p), and the rows of matrix Bmay be partitioned into partitions b₁-b_(p). Each partition may then bedistributed to a particular matrix processing chip. For example,partitions a₁ and b₁ may be distributed to a first matrix processingchip, partitions a₂ and b₂ may be distributed to a second matrixprocessing chip, and so forth.

Moreover, in some embodiments the matrix operands may be furtherpartitioned based on the hierarchical arrangement of processingresources, as described in connection with FIG. 5. For example, thepartition distributed to a particular matrix processing chip may then besimilarly partitioned and distributed across the matrix processingclusters of that matrix processing chip (e.g., matrix processingclusters 230 of FIG. 2B). The partition distributed to a particularmatrix processing cluster may then be similarly partitioned anddistributed across the matrix processing units (MPUs) of that matrixprocessing cluster (e.g., matrix processing units (MPUs) 234 of FIG.2C).

The weight update operation may then be performed as described inconnection with FIGS. 6B and 6C.

FIG. 6B illustrates the first stage of the weight update operation. Inthe first stage, each matrix processing chip may perform a partialmatrix multiplication operation using its respective partitions ofmatrices A and B. For example, the first chip may perform a partialmatrix multiplication operation using partitions a₁ and b₁, the secondchip may perform a partial matrix multiplication operation usingpartitions a₂ and b₂, and so forth. The partial result calculated byeach matrix processing chip may then be stored in the correspondinglocation in result matrix C.

Moreover, in some embodiments, the partial matrix operations may befurther distributed based on the hierarchical arrangement of processingresources. For example, the partial matrix operations distributed to aparticular matrix processing chip may then be similarly distributedacross the matrix processing clusters of that matrix processing chip(e.g., matrix processing clusters 230 of FIG. 2B). The partial matrixoperations distributed to a particular matrix processing cluster maythen be similarly distributed across the matrix processing units (MPUs)of that matrix processing cluster (e.g., matrix processing units (MPUs)234 of FIG. 2C).

While the partial operations are being performed by the matrixprocessing chips, each chip may simultaneously send and receive partialmatrix operands to and from its neighboring matrix processing chips. Forexample, in some embodiments, the matrix processing chips may beconfigured in a single-cyclical arrangement (e.g., with one-waycommunication between neighboring chips) or a dual-cyclical arrangement(e.g., with two-way communication between neighboring chips). In asingle-cyclical configuration, each matrix processing chip may send orreceive partial matrix operands to or from each neighboring chip.However, a single-cyclical configuration may be unable to achieve 100%processing efficiency for certain matrix operations and matrix operands(e.g., a large matrix operand which is neither square nor a singlevector, such as a “thin” matrix with a much larger height than width).In a dual-cyclical configuration, each matrix processing chip may sendand receive matrix operands to and from both neighboring chips.Accordingly, a dual-cyclical configuration may significantly reduce thelatency for communicating matrix operands, thus avoiding any idleprocessing time.

Using either approach, the partitions of matrix B (e.g., partitionsb₁-b_(p)) are shifted across matrix processing chips during each stageof partial matrix operations. For example, the illustrated embodimentuses a single-cyclical approach, such that each partition of matrix B(e.g., partitions b₁-b_(p)) is transmitted from its current chip to asingle neighboring chip. Other embodiments may use a dual-cyclicalapproach, such that each partition of matrix B (e.g., partitionsb₁-b_(p)) is transmitted from its current chip to both neighboringchips, thus reducing the latency for communicating partial matrixoperands by half.

In this manner, during each stage of partial matrix operations, partialmatrix operands (e.g., partitions b₁-b_(p)) are shifted to neighboringchip(s), and each matrix processing chip may then use the partial matrixoperands received from neighboring chips for subsequent partial matrixoperations, as described in connection with FIG. 6C.

FIG. 6C illustrates the second stage of the weight update operation. Inthe second stage, each matrix processing chip may perform a partialmatrix multiplication operation using its respective partitions ofmatrices A and B. For example, while the partitions of matrix A remainthe same across the chips, the partitions of matrix B have been shiftedacross the chips, as described in connection with FIG. 6B. Thus, thefirst chip may perform a partial matrix multiplication operation usingpartitions a₁ and b₂, the second chip may perform a partial matrixmultiplication operation using partitions a₂ and b₃, and so forth.Moreover, in some embodiments the partial matrix operations may befurther distributed based on the hierarchical arrangement of processingresources, as described in connection with FIG. 6B. The partial resultcalculated by each matrix processing chip may then be stored in thecorresponding location in result matrix C.

Moreover, while the partial operations are being performed by the matrixprocessing chips, each chip may simultaneously send and receive partialmatrix operands to and from its neighboring matrix processing chips, asdescribed in connection with FIG. 6B. For example, each matrixprocessing chip may send its current partition of matrix B (e.g.,partitions b₁-b_(p)) to one or more neighboring chips.

Thus, during each stage of partial matrix operations, partial matrixoperands (e.g., partitions b₁-b_(p)) are shifted to neighboring chip(s),and each matrix processing chip may then use the partial matrix operandsreceived from neighboring chips for subsequent partial matrixoperations. These stages of the matrix operation may continue in thismanner until all partial results for result matrix C have been computed.The result of the matrix operation may then be determined using thepartial results collectively computed by the matrix processing chips.

FIGS. 7A-C illustrate an example forward propagation operation in aneural network. FIG. 7A illustrates the forward propagation operationthat is to be performed, and FIGS. 7B and 7C illustrate how the forwardpropagation operation is performed.

FIG. 7A illustrates the following operation: A*B=C. A forwardpropagation operation may be implemented using the formula A₂=w*A₁,which may translate as follows in FIG. 7A: matrix A corresponds to w(e.g., the weight matrix); matrix B corresponds to A₁ (e.g., the firstactivation matrix); and matrix C corresponds to A₂ (e.g., the secondactivation matrix).

Matrices A and B may first be partitioned based on the number ofavailable processing resources, as described in connection with FIG. 5.For example, in some embodiments, matrices A and B may be partitionedinto P partitions corresponding to the number of available matrixprocessing chips (e.g., matrix processing chips 220 of FIG. 2A). Forexample, if there are P matrix processing chips, the rows of matrix Amay be partitioned into partitions a_(1x)-a_(px), and the rows of matrixB may be partitioned into partitions b₁-b_(p). Each partition may thenbe distributed to a particular matrix processing chip. For example,partitions a_(1x) and b₁ may be distributed to a first matrix processingchip, partitions a_(2x) and b₂ may be distributed to a second matrixprocessing chip, and so forth.

Moreover, in some embodiments the matrix operands may be furtherpartitioned based on the hierarchical arrangement of processingresources, as described in connection with FIG. 5. For example, thepartition distributed to a particular matrix processing chip may then besimilarly partitioned and distributed across the matrix processingclusters of that matrix processing chip (e.g., matrix processingclusters 230 of FIG. 2B). The partition distributed to a particularmatrix processing cluster may then be similarly partitioned anddistributed across the matrix processing units (MPUs) of that matrixprocessing cluster (e.g., matrix processing units (MPUs) 234 of FIG.2C).

The forward propagation operation may then be performed as described inconnection with FIGS. 7B and 7C. For example, the correspondingpartitions of result matrix C (e.g., c₁-c_(p)) may be calculated andstored by each matrix processing chip, such that c_(i)=Σ a_(ij)*b_(j).

FIG. 7B illustrates the first stage of the forward propagationoperation. In the first stage, each matrix processing chip may perform apartial matrix multiplication operation using its respective partitionsof matrices A and B. For example, the first chip may perform a partialmatrix multiplication operation using partitions a₁₁ and b₁, the secondchip may perform a partial matrix multiplication operation usingpartitions a₂₂ and b₂, and so forth. The partial result calculated byeach matrix processing chip may then be stored in the correspondingpartition c₁-c_(p) of result matrix C, such that c_(i)=a_(ii)*b_(i).

Moreover, in some embodiments, the partial matrix operations may befurther distributed based on the hierarchical arrangement of processingresources. For example, the partial matrix operations distributed to aparticular matrix processing chip may then be similarly distributedacross the matrix processing clusters of that matrix processing chip(e.g., matrix processing clusters 230 of FIG. 2B). The partial matrixoperations distributed to a particular matrix processing cluster maythen be similarly distributed across the matrix processing units (MPUs)of that matrix processing cluster (e.g., matrix processing units (MPUs)234 of FIG. 2C).

While the partial operations are being performed by the matrixprocessing chips, each chip may simultaneously send and receive partialmatrix operands to and from its neighboring matrix processing chips,using a single-cyclical or dual-cyclical configuration, as described inconnection with FIG. 6B. Thus, the partitions of matrix B (e.g.,partitions b₁-b_(p)) may be shifted across matrix processing chipsduring each stage of partial matrix operations. For example, theillustrated embodiment uses a single-cyclical approach, such that eachpartition of matrix B (e.g., partitions b₁-b_(p)) is transmitted fromits current chip to a single neighboring chip. Other embodiments may usea dual-cyclical approach, such that each partition of matrix B (e.g.,partitions b₁-b_(p)) is transmitted from its current chip to bothneighboring chips, thus reducing the latency for communicating partialmatrix operands by half.

In this manner, during each stage of partial matrix operations, partialmatrix operands (e.g., partitions b₁-b_(p)) are shifted to neighboringchip(s), and each matrix processing chip may then use the partial matrixoperands received from neighboring chips for subsequent partial matrixoperations, as described in connection with FIG. 7C.

FIG. 7C illustrates the second stage of the forward propagationoperation. In the second stage, each matrix processing chip may performa partial matrix multiplication operation using its respectivepartitions of matrices A and B. For example, while the partitions ofmatrix A remain the same across the chips, the partitions of matrix Bhave been shifted across the chips, as described in connection with FIG.7B. Thus, the first chip may perform a partial matrix multiplicationoperation using partitions a₁₂ and b₂, the second chip may perform apartial matrix multiplication operation using partitions a₂₃ and b₃, andso forth. Moreover, in some embodiments the partial matrix operationsmay be further distributed based on the hierarchical arrangement ofprocessing resources, as described in connection with FIG. 7B. Thepartial result calculated by each matrix processing chip may then beadded to the current value stored in the corresponding partitionc₁-c_(p) of result matrix C, such that c_(i)=c_(i)+a_(i(i+1))*b_(i+1).In this manner, when all partial operations are complete, each partitionc₁-c_(p) of result matrix C contains the sum of the partial resultscalculated by the corresponding matrix processing chip, such thatc_(i)=Σ a_(ij)*b_(j).

Moreover, while the partial operations are being performed by the matrixprocessing chips, each chip may simultaneously send and receive partialmatrix operands to and from its neighboring matrix processing chips, asdescribed in connection with FIG. 7B. For example, each matrixprocessing chip may send its current partition of matrix B (e.g.,partitions b₁-b_(p)) to one or more neighboring chips.

Thus, during each stage of partial matrix operations, partial matrixoperands (e.g., partitions b₁-b_(p)) are shifted to neighboring chip(s),and each matrix processing chip may then use the partial matrix operandsreceived from neighboring chips for subsequent partial matrixoperations. These stages of the matrix operation may continue in thismanner until all partial results for result matrix C have been computed.The result of the matrix operation may then be determined using thepartial results collectively computed by the matrix processing chips.

FIGS. 8A-C illustrate an example backward propagation operation in aneural network. FIG. 8A illustrates the backward propagation operationthat is to be performed, and FIGS. 8B and 8C illustrate how the backwardpropagation operation is performed.

FIG. 8A illustrates the following operation: A^(T)*B=C. A backwardpropagation operation may be implemented using the formula A₁=w^(T)*A₂,which may translate as follows in FIG. 8A: matrix A corresponds to w(e.g., the weight matrix); matrix B corresponds to A₂ (e.g., the secondactivation matrix); and matrix C corresponds to A₁ (e.g., the firstactivation matrix). In this example, the matrix operation A^(T)*B=C maybe performed without having to perform a transpose on the elements ofmatrix A in memory.

Matrices A and B may first be partitioned based on the number ofavailable processing resources, as described in connection with FIG. 5.For example, in some embodiments, matrices A and B may be partitionedinto P partitions corresponding to the number of available matrixprocessing chips (e.g., matrix processing chips 220 of FIG. 2A). Forexample, if there are P matrix processing chips, the rows of matrix Amay be partitioned into partitions a_(1x)-a_(px), and the rows of matrixB may be partitioned into partitions b₁-b_(p). Each partition may thenbe distributed to a particular matrix processing chip. For example,partitions a_(1x) and b₁ may be distributed to a first matrix processingchip, partitions a_(2x) and b₂ may be distributed to a second matrixprocessing chip, and so forth.

Moreover, in some embodiments the matrix operands may be furtherpartitioned based on the hierarchical arrangement of processingresources, as described in connection with FIG. 5. For example, thepartition distributed to a particular matrix processing chip may then besimilarly partitioned and distributed across the matrix processingclusters of that matrix processing chip (e.g., matrix processingclusters 230 of FIG. 2B). The partition distributed to a particularmatrix processing cluster may then be similarly partitioned anddistributed across the matrix processing units (MPUs) of that matrixprocessing cluster (e.g., matrix processing units (MPUs) 234 of FIG.2C).

The backward propagation operation may then be performed as described inconnection with FIGS. 8B and 8C. For example, the correspondingpartitions of result matrix C (e.g., c₁-c_(p)) may be calculated andstored by each matrix processing chip, such that c_(i)=A[:i]*B.

FIG. 8B illustrates the first stage of the backward propagationoperation. In the first stage, each matrix processing chip may perform apartial matrix multiplication operation using its respective partitionsof matrices A and B. For example, the first chip may perform a partialmatrix multiplication operation using partitions a₁₂ and b₁, the secondchip may perform a partial matrix multiplication operation usingpartitions a₂₃ and b₂, and so forth. The partial result calculated byeach matrix processing chip may then be stored in the correspondingpartition c₁-c_(p) of result matrix C.

Moreover, in some embodiments, the partial matrix operations may befurther distributed based on the hierarchical arrangement of processingresources. For example, the partial matrix operations distributed to aparticular matrix processing chip may then be similarly distributedacross the matrix processing clusters of that matrix processing chip(e.g., matrix processing clusters 230 of FIG. 2B). The partial matrixoperations distributed to a particular matrix processing cluster maythen be similarly distributed across the matrix processing units (MPUs)of that matrix processing cluster (e.g., matrix processing units (MPUs)234 of FIG. 2C).

While the partial operations are being performed by the matrixprocessing chips, each chip may simultaneously send and receive partialmatrix data to and from its neighboring matrix processing chips, asdescribed in connection with FIG. 6B. However, for a backwardpropagation operation, the partitions of result matrix C (e.g.,partitions c₁-c_(p)) may be shifted across matrix processing chipsduring each stage of partial matrix operations. For example, in theillustrated embodiment, each partition c₁-c_(p) of result matrix C istransmitted from its current chip to a neighboring chip.

In this manner, during the first stage of partial matrix operations,partial results are calculated and stored in the corresponding partitionc₁-c_(p) of result matrix C. Each partial result on partitions c₁-c_(p)is then shifted to a neighboring chip, and each matrix processing chipmay then use the partial result received from a neighboring chip forsubsequent partial matrix operations, as described in connection withFIG. 8C.

FIG. 8C illustrates the second stage of the backward propagationoperation. In the second stage, each matrix processing chip may performa partial matrix multiplication operation using its respectivepartitions of matrices A and B. In some embodiments, the partial matrixoperations may be further distributed based on the hierarchicalarrangement of processing resources, as described in connection withFIG. 8B.

As an example, the first chip may perform a partial matrixmultiplication operation using partitions a₁₃ and b₁, the second chipmay perform a partial matrix multiplication operation using partitionsa₂₄ and b₂, and so forth. The partial result calculated by each matrixprocessing chip may then be added to the current value of the resultpartition c₁-c_(p), which was previously received from a neighboringchip (as discussed in connection with FIG. 8B). For example, partitionc₂ may have previously been shifted from the second chip to the firstchip, and thus the first chip may now add that value of c₂ to thepartial result computed in the current stage (e.g., c₂=c₂+a₁₃*b₁).

While the partial operations are being performed by the matrixprocessing chips, each chip may simultaneously send and receive partialmatrix data to and from its neighboring matrix processing chips, asdescribed in connection with FIG. 8B. For example, each matrixprocessing chip may send its current partition of result matrix C (e.g.,partitions c₁-c_(p)) to a neighboring chip. Thus, during each stage ofpartial matrix operations, partial matrix results (e.g., partitionsc₁-c_(p)) are shifted to a neighboring chip, and each matrix processingchip may then use the partial matrix result received from a neighboringchip for subsequent partial matrix operations. These stages of thematrix operation may continue in this manner until all partial resultsfor result matrix C have been computed. In this manner, when all partialoperations are complete, the partitions c₁-c_(p) of result matrix Ccontain the result of the matrix operation A^(T)*B=C, allowing thematrix operation to be performed without having to transpose theelements of matrix A in memory.

FIG. 9 illustrates a flowchart 900 for an example embodiment ofdistributed matrix operations. Flowchart 900 may be implemented, in someembodiments, by components described throughout this disclosure (e.g.,the matrix processing architecture of FIGS. 2A-C).

The flowchart may begin at block 902 by receiving a command to perform amatrix operation. The matrix operation may comprise an operationassociated with a plurality of input matrices (e.g., matrix operands),such as one or more matrix multiplication operations. In someembodiments, the matrix operation may be associated with an operation ina neural network, such as a forward propagation operation, backwardpropagation operation, and/or weight update operation.

The flowchart may then proceed to block 904 to partition the inputmatrices into a plurality of partitions based on the number of availableprocessing elements. In some embodiments, the input matrices may bepartitioned based on the hierarchical arrangement of processingresources, as described further in connection with block 906. Moreover,in some embodiments, the input matrices may be partitioned across theirrows.

The flowchart may then proceed to block 906 to distribute the partitionsto the available processing elements. For example, in some embodiments,each partition may be distributed to a particular processing element.Moreover, in some embodiments, the processing elements may be configuredin a hierarchical arrangement with a plurality of processing levels, andthe matrix operation may be distributed across the hierarchy ofprocessing levels. For example, the processing elements may includemultiple matrix processing chips (e.g., matrix processing chips 220 ofFIG. 2A), multiple matrix processing clusters on each matrix processingchip (e.g., matrix processing clusters 230 of FIG. 2B), and/or multiplematrix processing units (MPUs) on each matrix processing cluster (e.g.,matrix processing units (MPUs) 234 of FIG. 2C). In those embodiments,the matrix operation may first be partitioned and distributed across thematrix processing chips. The partial matrix operation distributed to aparticular matrix processing chip may then be similarly partitioned anddistributed across the matrix processing clusters of that matrixprocessing chip. The partial matrix operation distributed to aparticular matrix processing cluster may then be similarly partitionedand distributed across the matrix processing units (MPUs) of that matrixprocessing cluster.

The flowchart may then proceed to block 908 to perform partial matrixoperations using the processing elements. For example, each processingelement may perform a partial matrix operation based on the matrix datadistributed to that processing element.

The flowchart may then proceed to block 910 to transmit partial matrixdata between processing elements while performing the partial matrixoperations. For example, in some embodiments, the processing elementsmay be configured in a cyclical arrangement such that each processingelement is communicatively coupled to multiple neighbor processingelements. Moreover, the partial matrix operations may be performed in aplurality of stages, and each processing element may transmit partialmatrix data to its neighbor processing elements while performing aparticular stage of the partial matrix operations. For example, in someembodiments, each processing element may transmit partial matrix data toone of its neighbor processing elements (e.g., using a single-cyclicalapproach) or to both of its neighbor processing elements (e.g., using adual-cyclical approach) during each stage of partial matrix operations.For example, a first processing element may use or calculate partialmatrix data in a particular stage of the partial matrix operations, thefirst processing element may transmit the partial matrix data to asecond processing element, and the second processing element may thenuse the partial matrix data in a subsequent stage of the partial matrixoperations. In some matrix operations, the partial matrix data mayinclude a partial input matrix, while in other matrix operations thepartial matrix data may include a partial result matrix.

The flowchart may then proceed to block 912 to determine a result of thematrix operation. For example, the result of the matrix operation may bedetermined based on the partial results collectively computed by theprocessing elements.

At this point, the flowchart may be complete. In some embodiments,however, the flowchart may restart and/or certain blocks may berepeated. For example, in some embodiments, the flowchart may restart atblock 902 to continue receiving and processing commands to performmatrix operations.

The flowcharts and block diagrams in the FIGURES illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousaspects of the present disclosure. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder or alternative orders, depending upon the functionality involved.It will also be noted that each block of the block diagrams and/orflowchart illustration, and combinations of blocks in the block diagramsand/or flowchart illustration, can be implemented by special purposehardware-based systems that perform the specified functions or acts, orcombinations of special purpose hardware and computer instructions.

The foregoing disclosure outlines features of several embodiments sothat those skilled in the art may better understand various aspects ofthe present disclosure. Those skilled in the art should appreciate thatthey may readily use the present disclosure as a basis for designing ormodifying other processes and structures for carrying out the samepurposes and/or achieving the same advantages of the embodimentsintroduced herein. Those skilled in the art should also realize thatsuch equivalent constructions do not depart from the spirit and scope ofthe present disclosure, and that they may make various changes,substitutions, and alterations herein without departing from the spiritand scope of the present disclosure.

All or part of any hardware element disclosed herein may readily beprovided in a system-on-a-chip (SoC), including a central processingunit (CPU) package. An SoC represents an integrated circuit (IC) thatintegrates components of a computer or other electronic system into asingle chip. The SoC may contain digital, analog, mixed-signal, andradio frequency functions, all of which may be provided on a single chipsubstrate. Other embodiments may include a multi-chip-module (MCM), witha plurality of chips located within a single electronic package andconfigured to interact closely with each other through the electronicpackage. In various other embodiments, the computing functionalitiesdisclosed herein may be implemented in one or more silicon cores inApplication Specific Integrated Circuits (ASICs), Field ProgrammableGate Arrays (FPGAs), and other semiconductor chips.

As used throughout this specification, the term “processor” or“microprocessor” should be understood to include not only a traditionalmicroprocessor (such as Intel's® industry-leading x86 and x64architectures), but also matrix processors, graphics processors, and anyASIC, FPGA, microcontroller, digital signal processor (DSP),programmable logic device, programmable logic array (PLA), microcode,instruction set, emulated or virtual machine processor, or any similar“Turing-complete” device, combination of devices, or logic elements(hardware or software) that permit the execution of instructions.

Note also that in certain embodiments, some of the components may beomitted or consolidated. In a general sense, the arrangements depictedin the figures should be understood as logical divisions, whereas aphysical architecture may include various permutations, combinations,and/or hybrids of these elements. It is imperative to note thatcountless possible design configurations can be used to achieve theoperational objectives outlined herein. Accordingly, the associatedinfrastructure has a myriad of substitute arrangements, design choices,device possibilities, hardware configurations, software implementations,and equipment options.

In a general sense, any suitably-configured processor can executeinstructions associated with data or microcode to achieve the operationsdetailed herein. Any processor disclosed herein could transform anelement or an article (for example, data) from one state or thing toanother state or thing. In another example, some activities outlinedherein may be implemented with fixed logic or programmable logic (forexample, software and/or computer instructions executed by a processor)and the elements identified herein could be some type of a programmableprocessor, programmable digital logic (for example, a field programmablegate array (FPGA), an erasable programmable read only memory (EPROM), anelectrically erasable programmable read only memory (EEPROM)), an ASICthat includes digital logic, software, code, electronic instructions,flash memory, optical disks, CD-ROMs, DVD ROMs, magnetic or opticalcards, other types of machine-readable mediums suitable for storingelectronic instructions, or any suitable combination thereof.

In operation, a storage may store information in any suitable type oftangible, non-transitory storage medium (for example, random accessmemory (RAM), read only memory (ROM), field programmable gate array(FPGA), erasable programmable read only memory (EPROM), electricallyerasable programmable ROM (EEPROM), or microcode), software, hardware(for example, processor instructions or microcode), or in any othersuitable component, device, element, or object where appropriate andbased on particular needs. Furthermore, the information being tracked,sent, received, or stored in a processor could be provided in anydatabase, register, table, cache, queue, control list, or storagestructure, based on particular needs and implementations, all of whichcould be referenced in any suitable timeframe. Any of the memory orstorage elements disclosed herein should be construed as beingencompassed within the broad terms ‘memory’ and ‘storage,’ asappropriate. A non-transitory storage medium herein is expresslyintended to include any non-transitory special-purpose or programmablehardware configured to provide the disclosed operations, or to cause aprocessor to perform the disclosed operations. A non-transitory storagemedium also expressly includes a processor having stored thereonhardware-coded instructions, and optionally microcode instructions orsequences encoded in hardware, firmware, or software.

Computer program logic implementing all or part of the functionalitydescribed herein is embodied in various forms, including, but in no waylimited to, hardware description language, a source code form, acomputer executable form, machine instructions or microcode,programmable hardware, and various intermediate forms (for example,forms generated by an HDL processor, assembler, compiler, linker, orlocator). In an example, source code includes a series of computerprogram instructions implemented in various programming languages, suchas an object code, an assembly language, or a high-level language suchas OpenCL, FORTRAN, C, C++, JAVA, or HTML for use with various operatingsystems or operating environments, or in hardware description languagessuch as Spice, Verilog, and VHDL. The source code may define and usevarious data structures and communication messages. The source code maybe in a computer executable form (e.g., via an interpreter), or thesource code may be converted (e.g., via a translator, assembler, orcompiler) into a computer executable form, or converted to anintermediate form such as byte code. Where appropriate, any of theforegoing may be used to build or describe appropriate discrete orintegrated circuits, whether sequential, combinatorial, state machines,or otherwise.

In one example, any number of electrical circuits of the FIGURES may beimplemented on a board of an associated electronic device. The board canbe a general circuit board that can hold various components of theinternal electronic system of the electronic device and, further,provide connectors for other peripherals. More specifically, the boardcan provide the electrical connections by which the other components ofthe system can communicate electrically. Any suitable processor andmemory can be suitably coupled to the board based on particularconfiguration needs, processing demands, and computing designs. Othercomponents such as external storage, additional sensors, controllers foraudio/video display, and peripheral devices may be attached to the boardas plug-in cards, via cables, or integrated into the board itself. Inanother example, the electrical circuits of the FIGURES may beimplemented as stand-alone modules (e.g., a device with associatedcomponents and circuitry configured to perform a specific application orfunction) or implemented as plug-in modules into application specifichardware of electronic devices.

Note that with the numerous examples provided herein, interaction may bedescribed in terms of two, three, four, or more electrical components.However, this has been done for purposes of clarity and example only. Itshould be appreciated that the system can be consolidated orreconfigured in any suitable manner. Along similar design alternatives,any of the illustrated components, modules, and elements of the FIGURESmay be combined in various possible configurations, all of which arewithin the broad scope of this specification. In certain cases, it maybe easier to describe one or more of the functionalities of a given setof flows by only referencing a limited number of electrical elements. Itshould be appreciated that the electrical circuits of the FIGURES andits teachings are readily scalable and can accommodate a large number ofcomponents, as well as more complicated/sophisticated arrangements andconfigurations. Accordingly, the examples provided should not limit thescope or inhibit the broad teachings of the electrical circuits aspotentially applied to a myriad of other architectures.

Numerous other changes, substitutions, variations, alterations, andmodifications may be ascertained to one skilled in the art and it isintended that the present disclosure encompass all such changes,substitutions, variations, alterations, and modifications as fallingwithin the scope of the appended claims.

Example Implementations

The following examples pertain to embodiments described throughout thisdisclosure.

One or more embodiments may include an apparatus, comprising: aplurality of memory elements to store matrix data; and a plurality ofprocessing elements to perform a matrix operation associated with aplurality of input matrices, wherein the plurality of processingelements is configured to: partition the plurality of input matricesinto a plurality of input partitions, wherein the plurality of inputmatrices is partitioned based on a number of available processingelements; distribute the plurality of input partitions among theplurality of processing elements, wherein each input partition isdistributed to a particular processing element of the plurality ofprocessing elements; perform a plurality of partial matrix operationsusing the plurality of processing elements; transmit partial matrix databetween the plurality of processing elements while performing theplurality of partial matrix operations; and determine a result of thematrix operation based on the plurality of partial matrix operations.

In one example embodiment of an apparatus: the plurality of processingelements is configured in a hierarchical arrangement comprising aplurality of processing levels; and the plurality of processing elementsis further configured to distribute the matrix operation across theplurality of processing levels.

In one example embodiment of an apparatus, the plurality of processingelements is further configured to partition the plurality of inputmatrices based on a number of rows of the plurality of input matrices.

In one example embodiment of an apparatus: the plurality of processingelements is configured in a cyclic arrangement such that each processingelement is communicatively coupled to a plurality of neighbor processingelements; and the plurality of neighbor processing elements of eachprocessing element comprises a first neighbor processing element and asecond neighbor processing element.

In one example embodiment of an apparatus, the plurality of processingelements is further configured to: perform the plurality of partialmatrix operations in a plurality of stages; and transmit a portion ofthe partial matrix data from each processing element to one or more ofthe neighbor processing elements while performing a particular stage ofthe partial matrix operations.

In one example embodiment of an apparatus, the plurality of processingelements is further configured to transmit the portion of the partialmatrix data from each processing element to the first neighborprocessing element and the second neighbor processing element.

In one example embodiment of an apparatus, the partial matrix datacomprises a partial input matrix, wherein the partial input matrix is tobe used by a first processing element in a particular stage of thepartial matrix operations, and wherein the partial input matrix is to beused by a second processing element in a subsequent stage of the partialmatrix operations.

In one example embodiment of an apparatus, the partial matrix datacomprises a partial result matrix determined by a first processingelement in a particular stage of the partial matrix operations, and thepartial result matrix is to be used by a second processing element in asubsequent stage of the partial matrix operations.

In one example embodiment of an apparatus, the matrix operationcomprises one or more matrix multiplication operations.

In one example embodiment of an apparatus, the plurality of processingelements comprises: a plurality of matrix processing chips; and aplurality of matrix processing clusters associated with each matrixprocessing chip.

In one example embodiment of an apparatus, the matrix operation isassociated with a forward propagation operation in a neural network.

In one example embodiment of an apparatus, the matrix operation isassociated with a weight update operation in a neural network.

In one example embodiment of an apparatus, the matrix operation isassociated with a backward propagation operation in a neural network.

One or more embodiments may include a method, comprising: performing amatrix operation associated with a plurality of input matrices, whereinperforming the matrix operation comprises: partitioning the plurality ofinput matrices into a plurality of input partitions, wherein theplurality of input matrices is partitioned based on a number ofavailable processing elements; distributing the plurality of inputpartitions among a plurality of processing elements, wherein each inputpartition is distributed to a particular processing element of theplurality of processing elements; performing a plurality of partialmatrix operations using the plurality of processing elements;transmitting partial matrix data between the plurality of processingelements while performing the plurality of partial matrix operations;and determining a result of the matrix operation based on the pluralityof partial matrix operations.

In one example embodiment of a method, the matrix operation comprisesone or more matrix multiplication operations.

In one example embodiment of a method: the plurality of processingelements is configured in a hierarchical arrangement comprising aplurality of processing levels; and the matrix operation is distributedacross the plurality of processing levels.

In one example embodiment of a method, the plurality of processingelements comprises: a plurality of matrix processing chips; and aplurality of matrix processing clusters associated with each matrixprocessing chip.

In one example embodiment of a method, the plurality of input matricesis further partitioned based on a number of rows of the plurality ofinput matrices.

In one example embodiment of a method: the plurality of processingelements is configured in a cyclic arrangement such that each processingelement is communicatively coupled to a plurality of neighbor processingelements; and the plurality of neighbor processing elements of eachprocessing element comprises a first neighbor processing element and asecond neighbor processing element.

In one example embodiment of a method, the plurality of partial matrixoperations is performed in a plurality of stages, and each processingelement transmits a portion of the partial matrix data to one or more ofthe neighbor processing elements while performing a particular stage ofthe partial matrix operations.

In one example embodiment of a method, the portion of the partial matrixdata is transmitted from each processing element to the first neighborprocessing element and the second neighbor processing element.

In one example embodiment of a method, the partial matrix data comprisesa partial input matrix, wherein the partial input matrix is used by afirst processing element in a particular stage of the partial matrixoperations, and wherein the partial input matrix is used by a secondprocessing element in a subsequent stage of the partial matrixoperations.

In one example embodiment of a method, the matrix operation isassociated with a forward propagation operation in a neural network.

In one example embodiment of a method, the matrix operation isassociated with a weight update operation in a neural network.

In one example embodiment of a method, the partial matrix data comprisesa partial result matrix determined by a first processing element in aparticular stage of the partial matrix operations, and the partialresult matrix is used by a second processing element in a subsequentstage of the partial matrix operations.

In one example embodiment of a method, the matrix operation isassociated with a backward propagation operation in a neural network.

One or more embodiments may include a system, comprising: a plurality ofmemory elements to store matrix data; a plurality of processing elementsto perform a matrix operation associated with a plurality of inputmatrices, wherein the plurality of processing elements comprises: a hostprocessor; one or more matrix processing chips; a plurality of matrixprocessors associated with the one or more matrix processing chips;wherein the plurality of processing elements is configured to: partitionthe plurality of input matrices into a plurality of input partitions,wherein the plurality of input matrices is partitioned based on a numberof available processing elements; distribute the plurality of inputpartitions among the plurality of processing elements, wherein eachinput partition is distributed to a particular processing element of theplurality of processing elements; perform a plurality of partial matrixoperations using the plurality of processing elements; transmit partialmatrix data between the plurality of processing elements whileperforming the plurality of partial matrix operations; and determine aresult of the matrix operation based on the plurality of partial matrixoperations.

In one example embodiment of a system, the system further comprises acommunication interface to communicate with one or more remote matrixprocessing chips over a communication network.

One or more embodiments may include at least one machine accessiblestorage medium having instructions stored thereon, the instructions,when executed on a machine, cause the machine to: perform a matrixoperation associated with a plurality of input matrices, wherein theinstructions that cause the machine to perform the matrix operationfurther cause the machine to: partition the plurality of input matricesinto a plurality of input partitions, wherein the plurality of inputmatrices is partitioned based on a number of available processingelements; distribute the plurality of input partitions among a pluralityof processing elements, wherein each input partition is distributed to aparticular processing element of the plurality of processing elements;perform a plurality of partial matrix operations using the plurality ofprocessing elements; transmit partial matrix data between the pluralityof processing elements while performing the plurality of partial matrixoperations; and determine a result of the matrix operation based on theplurality of partial matrix operations.

In one example embodiment of a storage medium, the instructions furthercause the machine to partition the plurality of input matrices based ona number of rows of the plurality of input matrices.

In one example embodiment of a storage medium: the plurality ofprocessing elements is configured in a cyclic arrangement such that eachprocessing element is communicatively coupled to a plurality of neighborprocessing elements; and the plurality of neighbor processing elementsof each processing element comprises a first neighbor processing elementand a second neighbor processing element.

In one example embodiment of a storage medium, the instructions furthercause the machine to: perform the plurality of partial matrix operationsin a plurality of stages; and transmit a portion of the partial matrixdata from each processing element to one or more neighbor processingelements while performing a particular stage of the partial matrixoperations.

In one example embodiment of a storage medium, the instructions furthercause the machine to transmit the portion of the partial matrix datafrom each processing element to the first neighbor processing elementand the second neighbor processing element.

One or more embodiments may include an apparatus comprising means toperform a method in any of the preceding examples.

One or more embodiments may include at least one machine accessiblestorage medium having instructions stored thereon, the instructions,when executed on a machine, cause the machine to: perform a method orrealize an apparatus from any of the preceding examples.

What is claimed is:
 1. An apparatus, comprising: a plurality of memoryelements to store matrix data, wherein the matrix data comprises aplurality of input matrices; and a plurality of processing elements toperform a matrix operation associated with the plurality of inputmatrices, wherein the plurality of processing elements is configured to:partition the plurality of input matrices into a plurality of inputpartitions, wherein the plurality of input matrices is partitioned basedon a number of available processing elements; distribute the pluralityof input partitions among the plurality of processing elements, whereineach input partition is distributed to a particular processing elementof the plurality of processing elements; perform a plurality of partialmatrix operations using the plurality of processing elements; transmitpartial matrix data between the plurality of processing elements whileperforming the plurality of partial matrix operations; and determine aresult of the matrix operation based on the plurality of partial matrixoperations.
 2. The apparatus of claim 1, wherein the matrix operationcomprises one or more matrix multiplication operations.
 3. The apparatusof claim 1, wherein: the plurality of processing elements is configuredin a hierarchical arrangement comprising a plurality of processinglevels; and the plurality of processing elements is further configuredto distribute the matrix operation across the plurality of processinglevels.
 4. The apparatus of claim 3, wherein the plurality of processingelements comprises: a plurality of matrix processing chips; and aplurality of matrix processing clusters associated with each matrixprocessing chip.
 5. The apparatus of claim 1, wherein the plurality ofprocessing elements is further configured to partition the plurality ofinput matrices based on a number of rows of the plurality of inputmatrices.
 6. The apparatus of claim 1, wherein: the plurality ofprocessing elements is configured in a cyclic arrangement such that eachprocessing element is communicatively coupled to a plurality of neighborprocessing elements; and the plurality of neighbor processing elementsof each processing element comprises a first neighbor processing elementand a second neighbor processing element.
 7. The apparatus of claim 6,wherein the plurality of processing elements is further configured to:perform the plurality of partial matrix operations in a plurality ofstages; and transmit a portion of the partial matrix data from eachprocessing element to one or more of the neighbor processing elementswhile performing a particular stage of the partial matrix operations. 8.The apparatus of claim 7, wherein the plurality of processing elementsis further configured to transmit the portion of the partial matrix datafrom each processing element to the first neighbor processing elementand the second neighbor processing element.
 9. The apparatus of claim 8,wherein the partial matrix data comprises a partial input matrix,wherein the partial input matrix is to be used by a first processingelement in a particular stage of the partial matrix operations, andwherein the partial input matrix is to be used by a second processingelement in a subsequent stage of the partial matrix operations.
 10. Theapparatus of claim 9, wherein the matrix operation is associated with aforward propagation operation in a neural network.
 11. The apparatus ofclaim 9, wherein the matrix operation is associated with a weight updateoperation in a neural network.
 12. The apparatus of claim 7, wherein thepartial matrix data comprises a partial result matrix determined by afirst processing element in a particular stage of the partial matrixoperations, and wherein the partial result matrix is to be used by asecond processing element in a subsequent stage of the partial matrixoperations.
 13. The apparatus of claim 12, wherein the matrix operationis associated with a backward propagation operation in a neural network.14. A method, comprising: performing a matrix operation associated witha plurality of input matrices, wherein performing the matrix operationcomprises: partitioning the plurality of input matrices into a pluralityof input partitions, wherein the plurality of input matrices ispartitioned based on a number of available processing elements;distributing the plurality of input partitions among a plurality ofprocessing elements, wherein each input partition is distributed to aparticular processing element of the plurality of processing elements;performing a plurality of partial matrix operations using the pluralityof processing elements; transmitting partial matrix data between theplurality of processing elements while performing the plurality ofpartial matrix operations; and determining a result of the matrixoperation based on the plurality of partial matrix operations.
 15. Themethod of claim 14, wherein the plurality of input matrices is furtherpartitioned based on a number of rows of the plurality of inputmatrices.
 16. The method of claim 14, wherein: the plurality ofprocessing elements is configured in a cyclic arrangement such that eachprocessing element is communicatively coupled to a plurality of neighborprocessing elements; and the plurality of neighbor processing elementsof each processing element comprises a first neighbor processing elementand a second neighbor processing element.
 17. The method of claim 16,wherein the plurality of partial matrix operations is performed in aplurality of stages, and wherein each processing element transmits aportion of the partial matrix data to one or more of the neighborprocessing elements while performing a particular stage of the partialmatrix operations.
 18. The method of claim 17, wherein the portion ofthe partial matrix data is transmitted from each processing element tothe first neighbor processing element and the second neighbor processingelement.
 19. A system, comprising: a plurality of memory elements tostore matrix data, wherein the matrix data comprises a plurality ofinput matrices; a plurality of processing elements to perform a matrixoperation associated with the plurality of input matrices, wherein theplurality of processing elements comprises: a host processor; one ormore matrix processing chips; a plurality of matrix processorsassociated with the one or more matrix processing chips; wherein theplurality of processing elements is configured to: partition theplurality of input matrices into a plurality of input partitions,wherein the plurality of input matrices is partitioned based on a numberof available processing elements; distribute the plurality of inputpartitions among the plurality of processing elements, wherein eachinput partition is distributed to a particular processing element of theplurality of processing elements; perform a plurality of partial matrixoperations using the plurality of processing elements; transmit partialmatrix data between the plurality of processing elements whileperforming the plurality of partial matrix operations; and determine aresult of the matrix operation based on the plurality of partial matrixoperations.
 20. The system of claim 19, further comprising acommunication interface to communicate with one or more remote matrixprocessing chips over a communication network.
 21. At least onenon-transitory machine accessible storage medium having instructionsstored thereon, the instructions, when executed on a machine, cause themachine to: perform a matrix operation associated with a plurality ofinput matrices, wherein the instructions that cause the machine toperform the matrix operation further cause the machine to: partition theplurality of input matrices into a plurality of input partitions,wherein the plurality of input matrices is partitioned based on a numberof available processing elements; distribute the plurality of inputpartitions among a plurality of processing elements, wherein each inputpartition is distributed to a particular processing element of theplurality of processing elements; perform a plurality of partial matrixoperations using the plurality of processing elements; transmit partialmatrix data between the plurality of processing elements whileperforming the plurality of partial matrix operations; and determine aresult of the matrix operation based on the plurality of partial matrixoperations.
 22. The storage medium of claim 21, wherein the instructionsfurther cause the machine to partition the plurality of input matricesbased on a number of rows of the plurality of input matrices.
 23. Thestorage medium of claim 21, wherein: the plurality of processingelements is configured in a cyclic arrangement such that each processingelement is communicatively coupled to a plurality of neighbor processingelements; and the plurality of neighbor processing elements of eachprocessing element comprises a first neighbor processing element and asecond neighbor processing element.
 24. The storage medium of claim 21,wherein the instructions further cause the machine to: perform theplurality of partial matrix operations in a plurality of stages; andtransmit a portion of the partial matrix data from each processingelement to one or more neighbor processing elements while performing aparticular stage of the partial matrix operations.
 25. The storagemedium of claim 24, wherein the instructions further cause the machineto transmit the portion of the partial matrix data from each processingelement to the first neighbor processing element and the second neighborprocessing element.